**Q1** In connection with a program that provides alternatives for youth who have a run in with the criminal justice system, a colleague mentions that the program could be more effective if there were an easy way to predict who might benefit from the alternative program. The data suggests that about 75% of the youth in Ourtown are "good kids" who would benefit from the alternative program and 25% are "bad kids" who will not. Your supervisor also says you should come up with some more acceptable terms than "good" and "bad."

It turns out that when a kid is, in fact, "bad," the test gets it right 90% of the time, wrong 10%. But when the kid is, in fact, "good," the test says "bad" 30% of the time.12. Sketch an event tree that captures this and then flip the tree to evaluate the test and provide guidance on how to interpret its results.

**Q2** Sketch, anew, the decision tree for the embassy party described in the text book.

"The officer in charge of a United States Embassy recreation program has decided to replenish the employees club funds by arranging a dinner. It rains nine days out of ten at the post and he must decide whether to hold the dinner indoors or out. An enclosed pavilion is available but uncomfortable, and past experience has shown turnout to be low at indoor functions, resulting in a 60 per cent chance of gaining $100 from a dinner held in the pavilion and a 40 per cent chance of losing $20. On the other hand, an outdoor dinner could be expected to earn $500 unless it rains, in which case the dinner would lose about $10" (Stokey & Zeckhauser 1977, 202).

**Q3** What is the expected value of a two dice toss if the payoff is whatever comes up on the dice, in dollars? Sketch this as a decision tree with just chance nodes.

**Q71.** Consider this little bit of logic that describes a tourist's thinking process (taken from the title of a 1970s movie): “if it’s Tuesday, this must be Belgium. Otherwise, I have no idea where we are.” Sketch a flowchart that represents this flow of thought.

**Q72.** Sketch a flowchart that represents this bit of logic: “if you are a woman then if you are over 40 you should have this test no matter what but if either parent had diabetes women should have the test no matter what. Men only need to take the test if they are overweight.”

**Q73.** Sketch a flowchart that represents this bit of logic: “if cell E$3 is greater than cell G$12 then value is G$12; otherwise, value is G$12-E$3.”

**Q74.** Sketch a flowchart that represents this bit of logic: “if the balance is less than the minimum alternative payment then just pay the balance, otherwise, pay the minimum alternative payment.”

**Q75.** Sketch a flowchart that represents this bit of logic: “If you can get a direct flight for under $1500 take it unless it leaves from SFO before 9 am. Otherwise, see if anything is available on frequent flier miles no matter what the routing. If you can’t find anything, use Expedia to find the cheapest flight out of OAK.”

**Q76.** Sketch a flowchart that represents this bit of logic: If I have anything that is due tomorrow then if I am acing the class already and if I have some money I’ll go out drinking by myself (since all my friends will be busy), but if I don’t have any money I’ll stay home and watch reruns on cable. If, on the other hand, I’m not acing this class, I’ll stay home and study. If I don’t have anything due tomorrow, then if I have some money I’ll see if some friends are around and if so I’ll party with them. Otherwise, I’ll drink alone. If I don’ t have any money I’ll just stay home and watch reruns on cable.

**Q77.** Draw a flow charts that represents "Do A until B" and "While B do A. Then do C".

**Q78.** Sketch a flow chart that represents the following writing protocol: (1) Edit your essay until it is perfect. (2) While the essay still needs work, edit your essay.

**Q79.** Use stepwise refinement to create a flow chart for this set of instructions: Do A and then B. If C, then while E do F and after that do G, otherwise do H. Do I.

**Q80.** If A: until B do C and then, do D if E, otherwise do F while G. Otherwise if H, then if I do J else do K. Do L.

**Q81.** Is a picture worth 548 words? Convert the Rock County, Wisconsin "Drug Court Flow Chart" from text form to diagram form.

- District Attorney and Defense Attorney present to Judge in assigned Criminal Court a completed Rock County Drug Court Contract and a copy of the defendant’s criminal history (either NCIC Report or CCAP Record of Convictions).
- Criminal Court Judge determines the defendant may be eligible for Drug Court so the matter is continued for two (2) weeks before the same court. Judge orders defendant to attend an initial screening at the offices of the Rock County Community RECAP Program, 303 W. Court Street, Janesville, WI on the following Tuesday.
- Court Attendant for the Criminal Court will then immediately photocopy the completed Drug Court Contract, the defendant’s criminal record (either NCIC or CCAP), and the criminal complaint in the present matter and place them in an envelope and put it in the mailbox of the Community RECAP Program that is located in the Courthouse mailroom.
- The Court Attendant will daily FAX a list of the defendants referred the Community RECAP Program, providing the defendant’s name, date of birth, and case number. This will be FAXed daily to (608)743-1759 to provide that office with a list of the defendants they should expect the following Tuesday for the initial screening.
- Upon completion of the initial screening the Community RECAP office will FAX to the Criminal Court a document indicating the completion of the initial screening and whether the defendant is qualified for the Drug Court. If the defendant is eligible, the Community RECAP office will provide the defendant with an appointment date (scheduled after his next scheduled return to the Criminal court) for completion of the intake process and to complete a full assessment of the defendants needs. The defendant will also be scheduled with an initial date for first appearance at Drug Court. This information will also be contained in the FAX sent to the Criminal court.
- After the initial screening, the defendant returns to the Criminal Court. If the Community RECAP FAX (from #5 above) has been received by the court and it indicates that the defendant is eligible for the Drug Court, then the Criminal Court will take the plea to the original charge but will withhold a finding of guilt. The Court will then order the clerk to place the file in status “Deferred Pending”, continue bond and order the defendant to the Drug Court appearance indicated on that FAX.
- The Court Attendant will then photocopy the following documents, place them in an envelope, and forward them to Judge John Roethe of the Drug Court as these documents will constitute the Drug Court file:
- Criminal complaint,
- Completed Drug Court Contract,
- NCIC or CCAP criminal history of the defendant,
- Community RECAP Program FAX indicating the completion of the initial screening and initial date for first appearance before the Drug Court.

- The matter will not return to the Criminal Court until the defendant either successfully completes the program or is removed from the program. If the defendant successfully completed the program the court will implement the agreement outlined in the Drug Court Contract. If for any reason the defendant fails to complete the program the defendant’s original plea will be perfected the entry of a finding of guilt and the matter will proceed to sentencing on the original charge.

**Q82.** Flow chart the following protocols. (a) Record youth name and address. Check in system to see if already there. If there, pull up record and verify information. If not, create new record and ask for information. When done, send record to orientation staff, give youth a number and instruct to wait until number is called. (b) Once stage three in the treatment regimen is completed, clients are not eligible for the next stage in treatment until they have had three consecutive clean weekly drug tests. If they have one failed test they are given a warning. Two failed tests in a row and they have to meet with a counselor. Three failed tests and they are out of the program.

**Q83.** Weimer & Vining (1989) characterize policy problems in terms of market failure and government failure. Any given problem, they suggest, can be placed in one of four categories: (1) market AND government failure; (2) government works (policy corrects for market failure); (3) market works; (4) government failure to correct for market failure. Their suggested strategy is to start by asking whether there is a market failure and then whether there is government failure. Using the two conditionals, "Is there evidence of market failure?" and "Is there evidence of government failure?" construct a flowchart that would permit you to classify any given situation into one of the four aforementioned categories.

**Q84.** If the weather is nice, plant a garden. Otherwise paint the office. For the garden, make a decision between flowers and vegetables. If you go for vegetables, buy compost, seeds, and stakes; till the soil, and hook up the irrigation. If it's flowers this year, go to the garden store and if they have 4 inch plants buy enough for the plot and plant them. If they don't then get flats of smaller plants and bring them home and let them get acclimated for a week and then plant them next week. To till the soil, if the ox is healthy, do it with the animal plow, otherwise get out the rototiller.

**Q85.** A regimen consists of three mandatory sessions, followed by an optional weekend retreat and then, monthly sessions until standard test indicates absence of symptoms.

**Q86.** Sort clients into four categories promising, troubling, recalcitrant, hopeless on the basis of two tests which can be passed or failed.

**Q87.** Sketch a flow chart to represent the following scenario. The Alameda County Waste Management Authority (ACWMA) has decided to spend some money on a public relations campaign to increase the level of composting ("green bin") recylcing. Data on hand says that current levels are 4 kg per household of four per week. The plan is to spend $10,000 on advertising each month until the level has gone over 6 kg per week for four weeks in a row.

Prefatory concern – what does 4 kg / household of 4 / week mean? The amount of compost likely depends on the number of people in a household. We don't want to get the numbers wrong by failing to take this into account. So, in our data collection, we double the number for households of 2, halve it for households of 8, etc. Why not just express it as "kg/person/week"? That would work fine mathematically. Perhaps the PR folks had wanted to focus on households (and families) so as to induce a greater sense of collective responsibility.

**Q88.** Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

If the calculated payment (CALC_PMT) is less than the alternative monthly minimum payment (ALT_MIN_PMT) then the payment is the alternative monthly payment otherwise it is the calculated payment.

**Q89.** Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

If the current balance (BAL) is less than the calculated payment then pay the balance off, otherwise, pay the calculated payment.

**Q90.** Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

If the calculated payment is less than the alternative minimum monthly payment then pay the alternative monthly minimum unless it is more than the remaining balance in which case just pay the balance off. Otherwise pay the calculated payment.

**Q91.** Sketch flow chart that captures logic of the following process.

Organization consists of intake personnel, counselors, followup social workers, and clerical staff.

When a new client contacts the organization intake personnel determine which of four types of case it is by asking two questions. If a client is returning having already been "typed" she is sent to the appropriate waiting room. Types 1 and 3 are referred to counselor A, type 2 to counselor B, type 4 to counselor C.

Client goes to waiting room until counselor is free. Sessions take 1 hour so the wait can be long. If more than one person waiting client is advised to go away and come back later.

In session, if the client is over 18 they get treatment protocol 1 otherwise they get treatment protocol 2.

**Q92.** What is wrong with the decision tree here? I need to decide whether to work at home or go down to Stanford today. At home, because of distractions, I work at about 75% efficiency. If I go to my research office at Stanford I work at 100% efficiency. If I work at home I will get 8 hours to work. If I decide to drive down to Stanford, I will get 8 hours minus driving time to work. The normal drive is 60 minutes each way. But about 20% of the time it is extra light and the round trip takes just 90 minutes. About 30% of the time, though, traffic is awful and round trip is 180 minutes. I made a decision tree to figure out where I should work if I am trying to maximize my output, but I did something wrong. Fix the tree and tell me what I should do.

**Q93.** A new device at your favorite big box store costs $200. It has a one year guarantee from the manufacturer. The cashier offers you a special deal on a three year replacement warranty (assume it's good, will be honored, etc.) — $40. You estimate that the chances of the device failing during second and third years is 25% and that the price of replacement by then will be $150. Should you buy the service plan? What are the parameters of this decision model?

**Q94.** Assuming you are self-interested, what makes more sense: buy a $1.00 lottery ticket with a 1 in five million chance of winning a million dollars, buying a twenty dollar raffle ticket for a local fundraiser with a 1 in 2500 chance of winning a $500 jackpot, or playing a $1 stake game of rock-scissors-paper with the person next to you.

**Q95.** You never know what the weather is going to be around here. Somedays you need a sweater and some days you need sunglasses. The smart person, they say, always brings both. But suppose there is a definite hassle involved in bringing either (e.g., you ride a bike and space is tight). Sketch a decision tree that takes into account a cost to bringing either and a cost to not having either when you need them and the possibility that on a given day you might need one, the other, or both. Use plausible numbers of your own choice.

**Q96.** A college enrolls two types of students. Full-pay students pay $40K tuition and half-pay students pay $20K. At present the school spends $1 million per year to recruit 200 students about 75% of whom are half-pay and 25% full-pay. A consultant submits a proposal to shift resources around and use GIS to target recruitment at zip codes that are more likely to yield full-pay students. She says there is a 75% chance that the results will be a slightly smaller class (190) but one with 40% full-pay and 60% half-pay. Unfortunately there is also a risk things won't turn out so well. There's a 25% chance that enrollment will drop to 170 and only 30% will be full pay. Use a decision tree to advise the college as to its best course of action.

**Q97.** There's an idea in philosophy called "Pascal's Wager" that describes a way of thinking about the existence of god. It goes like this. I have a choice to believe or not believe. And there is a chance that god exists and a chance that there is no god. If I believe and there is a god, I have a chance at eternal salvation. If I don't believe but there is a god, I suffer eternal damnation. If I do believe and it turns out there is no god, I will feel a bit of a chump, but the atheists can feel smug if opposite is the case. Sketch this situation as a decision tree. Should you believe in god?

**Q98.** Sketch the decision tree for the following scenario. I want to buy a used car. The car I am looking at is being offered at $4000. The seller says it is in good shape all around. I look it over and agree, but you never know for sure. Suppose there is a 10% chance that it is a total dog and that buying it will be a $2000 mistake. I know a mechanic who will give it a very thorough inspection, for a price. If my assumptions are correct, what's the most I should pay my mechanic?

**Q99.** We want to apply for a home equity line of credit. The bank says it has to know what your house is worth (It has to be worth a certain amount over what we still owe on the mortgage to get a loan at a good rate). A loan at a bad rate will cost $10,000 more than a loan at a good rate. We think there is a 60:40 chance that our house is in fact worth enough to get a good rate. We have a choice between a cheap appraisal ($100) and an expensive appraisal ($1000). A cheap appraisal, we have learned, has a 40% chance of correctly valuing a property. An expensive appraisal is right 70% of the time. Draw a decision tree that will help us figure out what to do.

**Q100.** How much would you be willing to pay for a forecast that would resolve the contingency in problem 95?

**Q101.** If the farmer plants early and the spring is warm, she can get a 20% increase in her harvest. But if she plants early and there's a late frost she can lose 50% of her harvest. Historically, these late frosts happen one year in four (25% of the time). Use a decision tree to determine how much she would be willing to invest in a perfect forecast.

**Q102.** Kids these days! Of those who get into trouble, it turns out, about 30% are "real trouble-makers" who need some help. The other 70% are normal adolescents who will age out of their trouble-making under normal care. A social worker friend introduces you to a test that you can give to kids who are referred to you to determine which category they are in. Research has suggested the test is 75% accurate. Use tree flipping to describe what to make of the test's results.

**Q103.** Suppose we are running a program to which we want to accept only individuals in the top 25% of the population (on some measurable trait). Unfortunately, our test for measuring the trait is only 80% accurate. Draw event tree and flip to show what kind of faith we can have in the test results. Which test result appears more worthy of taking at face value? Which group would you be inclined to develop a second test for?

**Q104.** House gets another case. There's this funny rash. We won't say where it appears, but it's a funny rash. In 1% of the cases, it means something really, really bad — anxoreisis. Fortunately, there's a test. Unfortunately, it's not a perfect test. Fortunately, it's a pretty good test. Unfortunately, it is wrong 2% of the time. Work it out.

**Q105.** Following on problem 104, suppose the test is not painless or without its own risks. Suppose the "cost" of the test is 5. And suppose the treatment is also not so nice and the cost of the treatment is 15. But if you have the disease and you are not treated, the results are nasty : 50. Do we have enough information to recommend a course of action? What should we do?

**Q106.** She may love you or she may not. It turns out there is a 40% chance she does. You decide to use the buttercup test to find out (hold a buttercup under chin and see if it reflects yellow). The test is 90% accurate. Draw tree and flip to determine what conclusions we can draw from positive and negative buttercup test results.

**Q107.** Our neighborhood association has a ten member board. Each year it plans to add four members. Write the difference equations that describe the size of the board (S) each year.

**Q108.** You are a small non-profit. Your sole funder says that each year it will double what you have as your balance at the end of the year. Each year you project spending 20,000 for programs. Ignore interest. Write difference equations describing your balance (B).

What special situations can you imagine we might get into? What, for example, happens if B_{0}=$32,000? What happens if it is 50,000? 40,000?

**Q109.** Each year the feral cat population grows by 3%. Let C_{n} be the number of cats n years from now. Assume there are presently 350. Write a difference equation that describes the cat population from year to year.

**Q110.** Each year the feral cat population grows by 3%. Let C_{n} be the number of cats n years from now. Assume there are presently 350. Suppose that each year we catch and euthanize or place in homes 20 cats. Write the equations for this situation.

**Q111.** Let's say we have a 2 year graduate program. The first year class is growing at a rapid rate 5% per year. Between the first and second years, 25% of the students change their minds or get jobs and leave the program. Among the second years, 10% leave before graduation. The program currently has 20 first year and 12 second year. Write difference equations to describe population in future years.

**Q112.** Sketch a causal loop diagram representing this logic:

Being sad…

- …makes you frown…
- …which makes people avoid you…
- …which makes you lonely…
- …which makes you sad…

**Q113.** Sketch a causal loop diagram for this system (be sure to label each link and the overall loop). Comment on the long term equilibrium of this system.

- Being happy…
- …makes you to smile…
- …makes people approach you…
- …makes you feel social…
- …makes you happy…

**Q114.** A totalitarian country that prohibits migration has a birth rate **b** and a death rate **d**. How does the population change from one year to the next?

We can interpret "birth rate" or "death rate" in two ways — as a rate, for example, deaths per 100 people — or as an absolute number, for example, 5 people per year. In general, we will mean the former.

Let $P_{i}$ be the population in year **i**. Write an expression for the population in year i+1. If the population in a given year is 100 and birth rate, b, is 5% and the death rate, d, is 6%, write out the population for the next 5 years.

**Q115.** There are no births in a Shaker community, only **R** recruits per year. The death rate is **d**. What is the difference equation that describes this situation?

**Q116.** The Eastville School Committee is agrees to an annual $200 per year salary increase for each Eastville teacher. Express this as a difference equation.

**Q117.** The Westtown School committee is more generous. It agrees to a 5.5% cost-of-living increase per year, plus a one time only $200 adjustment for past sins of omission. Express this as a difference equation.

**Q118.** The Westtown School committee is more generous. It agrees to a 5.5% cost-of-living increase per year, plus a one time only $200 adjustment for past sins of omission. How much would it be worth to teachers if the one time adjustment were made before the first COLA rather than after.

**Q119.** Mills public policy program recruits **R** new students each fall. In the spring 0.0G (i.e., G%) students graduate. At the end of a typical year 0.0L (i.e., L%) of active students leave for personal or other reasons. Express the current student population, **P**, in terms of these figures.

**Q120.** My bathtub fills at 10 gallons per minute. It has a leak, though, whereby it loses 10% of it's volume per minute. It's a neat rectangular tub in which each 10 gallons is 2 inches of depth. How does it behave over time?

**Q121.** Consider a "leaky" reservoir. Current volume 1,200 million gallons. Inflow 200 million gallons per month. Consumption 150 million gallons per month. Leakage 5% of current volume per month.

- Draw a stock and flow diagram of the situation.
- Draw a causal loop diagram showing the relationship between reservoir volume and the net in/out flow.
- Identify amount(s) and rate(s).
- Write the difference equation in the form $P_{n+1} = a \times P_n + b$.
- Calculate the expected equilibrium.
- Set up Excel model.
- Chart reservoir volume vs. time.

**Q122.** The most basic opportunity cost incurred when undertaking a project is the simple value of investing the money instead of spending it. A first step toward figuring out what that cost is is understanding compound interest. Show what happens to $1000 if the annual interest rate is 5%.

**Q123.** Suppose I am sitting on $20,000 and I am trying to figure out whether or not to use it to buy a car. I have a very limited life and have determined that if I buy the car I will have to pay $800 insurance and about 10 cents per mile to operate it and I drive 2500 miles per year. If I own a car I'll drive rather than take the bus on approximately 300 local commutes (saving $1000 and 150 hours net). My time is worth $50 per hour. An alternative would be to put the $20,000 into an investment vehicle (so to speak) that would pay me 7.5% annually.

**Q124.** On the grid below …

…draw the line $y=2x + 1$

…shade the area for $x>5$ and the area for $y < 3$

…shade the area for y >= 2x + 1

**Q125.** Write an equation for the line passing through the points (3,2) and (0,5).

**Q126.** Why do people scream into cell phones? Answer in terms of feedback.

**Q127.** Consider the singles bar scene. Develop a model along the lines of the market for lemons (Wikipedia), that would suggest that information asymmetries could possibly kill the scene. What institutional interventions prevent this from happening?.

**Q128.** Consider the act of filling up a bathtub for a baby (or yourself!). You have a faucet that you can turn more towards hot or toward cold. List out the flows, the stocks, the sources of information, the "valves," and the rules that govern the valves in this system.

**Q129.** Draw a stock and flow diagram for filling up a bathtub for a baby (or yourself!). You have a faucet that you can turn more towards hot or toward cold. Be sure to show the flows, the stocks, the sources of information, the "valves," and the rules that govern the valves in this system.

**Q130.** In a "bathtub problem," why don't we include the water company or the sewer system to be stocks?

**Q131.** Draw a causal loop diagram that illustrates the process of feeling hungry, eating, becoming satisfied, stopping, getting hungry again.

**Q132.** Create both a causal loop and a stock and flow diagram for a thermostat, heater, and house. The house is a stock of air. When its temperature goes below some threshold, hot air is added. All along though, hot air is subtracted (or cold air is added) through leaky windows and the like. But the temperature does not change immediately upon introduction of the hot air. What are the challenges of modeling this phenomenon discretely and how can we solve them?

**Q133.** College is a more or less four year endeavor but students come and go on different schedules. Sketch a stock and flow model that shows freshwomen applicants coming from the cloud, admitted students from applicants, and freshwomen from the admittees. Then freshwomen become sophomores, mostly, but there is some attrition. And so on through the other years. Sketch a stock and flow diagram that follows students through four years and think up some variables that might affect the flows between the different years. For this problem, you should try wearing the hat of an academic administrator who is interested in the problems of "retention" and "degree completion."

**Q134.** Consider a system for a flu vaccine clinic. People arrive at some random or fixed rate and queue up. Our first station (F) has to get them to fill out a form, sign some papers, etc. After this they get in the line for the actual shots (at station V). We have a fixed number of staff whom we will divide between the two stations, depending on the size of the queues. Draw the stock and flow diagram for the system and write the equations for Q1, Q2, F and V.

**Q135.** Walk us through this diagram

**Q136.** Write out the difference equation that represents the following scenario and the first five terms of the corresponding sequence given the stated starting value.

- Membership in a club goes up by 4 people each year. At year one it has 21 members.
- A community's population increases by 4% each year. At year one it is 350.
- A swimming pool, currently containing 100,000 gallons of water, is leaking at the rate of 2% per day but is being filled at the rate of 1,000 gallons per day.
- A retirement account which stands at $120,000 earns 3% interest annually. The owner needs to withdraw $1500 per month to pay for eldercare.

For each of these, graph P_{n} vs. time.

For each of these, graph P_{n+1} vs. P_{n}

**Q137.** Derive the equation for the equilibrium value of a difference equation from a formula that shows how P_{n+1} relates to P_{n}.

**Q151.** A cinema has a marquee with lots and lots of light bulbs. In any given week 1% of the light bulbs burn out. Unfortunately, between being busy and being sloppy, replacement is a little bit sporadic. Of all the bulbs that are burnt out, about 95% get replaced each week. Draw the state diagram for this system.

**Q152.** Translate this description into a state diagram. A population consists of people who play it safe, and daredevils. From year to year, most (97%) safe-players stay that way, but 2% turn into daredevils. About 1% of the safe-players die each year. By contrast, 10% of daredevils die each year and another 10%, seeing that, switch to playing it safe. All the other daredevils stick with the program.

Label each of the states in as *transient* or *absorbing*.

**Q153.** A criminologist and an activist decide to collaborate on a project designed to reduce prison population. In the spirit of starting simple, they identify 4 states in which people can find themselves: never imprisoned; incarcerated; on parole; post-parole. The period of time in their analysis will be one year. Suppose 70% of the population has never been incarcerated. Each year 2% of these people are imprisoned. Of those currently incarcerated, 20% are released each year onto parole. Average parole is 5 years so that a person on parole has a 20% chance of finishing parole. Those on parole have a 10% chance of finding themselves back in prison in any given year. Individuals who are post parole have a 4% chance of returning to prison in any given year. Draw a state diagram and matrix representing this information.

**Q154.** Suppose a given housing market has a 10% turnover rate each year. How many houses will typically be in the first, second, third, etc. year of their mortgage at any given time? Assume 10 year mortgages to keep things simple. Draw the diagram that would be the first step in solving this problem.

**Q155.** Suppose 25% of the mortgages written in the first years of this century were subprime (meaning the borrowers were not very credit-worthy) and all were 5 year adjustable such that after the fifth year the monthly payments would go way up. In the market in question there is approximately 5% turnover housing each year. The housing stock in the market consists of one million units. Research has shown that 33 1/3% of subprime adjustable mortgages go into default under current conditions when they go past their five year mark (and these conditions are expected to continue for some time) when they adjust.

**Q156.** A state corrections system has established a new drug treatment facility for first offenders. The center has a capacity of 1000.

Inmates may leave the facility in either of two ways. In any period, there is a 10 percent probability that an inmate will be judged rehabilitated, in which case s/he will be released at the beginning of the following period.. There is also a 5 percent chance that an inmate will escape during each period. Rehabilitated addicts have a 20 percent chance of relapsing in each period; escapees have a 10 percent chance of being recaptured each period. Both recidivists and recaptured escapees are returned to the facility and have priority over new offenders.

Questions

If it operates at full capacity, how many of the original inmates will be resident at the facility 10 periods later?

How many new offenders can be admitted during each of the next 2 periods?

What happens if we modify the model to allow for a small possibility of death or a change in the probability of relapse?

**Q157.** Sketch the transition matrix that corresponds to the following diagram

**Q158.** Suppose the following statements are true about the local housing market.

- On a month to month basis, 90% of mortgage payments are on time, 10% are late or missed.
- Of all the late/missed payments, 25% are back on track the following month. 65% are late again. 10% go into default.
- Of all mortgages in default in a given month, 20% have a work-out and return to good standing. 70% remain in default and 10% move into foreclosure.
- Of all houses in foreclosure each month, the banks manage to get 20% back on the market and resold.

Draw the transition diagram and write out the transition matrix.

**Q159.** Implement the model from problem 158 using this Excel spreadsheet.

**Q164.** Sketch a flowchart that represents the logic of setting up a Schelling "tipping model":

To Create Schelling Model

- Set up the model.
- Run the model until everyone is content to stay where they are.

To Set Up

- Start with an NxN grid.
- Identify a number of type A residents and a number of type B residents such that A+B is less than N
^{2}. - Randomly place As and Bs on grid.

To Run the Model

- For each resident, evaluate move/stay choices
- For each resident, find new location for all those that choose move.

To Evaluate choice

- Identify the resident
- Count all neighbors
- Count similars
- Compute ratio
- If larger than threshold, mark as stay, otherwise mark as move

To Move

- Select a random square
- If empty, move there. Otherwise try again.

**Q165.** What's the difference between an "equation-based model" and an "agent model"? What are some other synonyms we might hear for these terms?

**Q166.**Consider a one dimensional cellular automata that looks like this:

Generation 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Generation 2 |

Show what the next few generations would look like subject to "rule 93":

Rule 93 | ||||||||||||||||||||||||||||||

0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |

**Q167.** Suppose we have a diffusion process in which all susceptibles who are in contact with an infected in a given time period become infected in the next time period. On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

**Q168.** Suppose we have a diffusion process in which susceptibles who are in contact with an infected in a given time period have a 50% chance of becoming infected in the next time period. Now play the “game” again except this time flip a coin each time (or use a random number chart for probabilities other than 50:50) to see whether neighbors become infected or not. Note: You might not want to play all the way out to time period 5! On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

**Q169.** Consider the 12 block neighborhood bounded by parks on the north and south and major thoroughfares on the east and west. Green houses are supporting Obama, purple houses Romney.

Using the facing blocks delineated by the red dashed lines as units (it yields 15 of them), calculate the index of dissimilarity.

**Q170.** Suppose you have a population of one hundred persons. It is divided into five categories of willingness to join a protest all of which depend on people's expectations of how many others will appear at the protest. The thresholds range from very low (I'll go if anyone else is going) to the very high (I won't go unless basically everybody else is going).

Assume the population is divided among these categories as follows:

Challenge of Recruiting | Very Easy | Easy | Average | Hard | Very Hard |
---|---|---|---|---|---|

Participation Threshold | 1 | 10 | 40 | 60 | 99 |

Number at this threshold | 10 | 20 | 40 | 20 | 10 |

a. If news reports suggest that 15 people will show up, how many actually will?

b. If last week saw participation of 41 and this is widely reported so that everyone knows, how many will come out this week? And then next week? And after that?

c. What if 91 came last week?

**Q171.** A common phrase to describe processes in which people engage in imitative behavior is "bandwagon effect." Explain the appropriateness of this metaphor.

**Q172.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

**Q173.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

**Q174.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. How does this system behave when the expected number is 10? 20? 50? 60? 90?

**Q175.** Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. Plot the cumulative distribution on a chart with a 45 degree line.

**Q176.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

**Q177.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

**Q178.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

**Q179.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

**Q180.** Which of the cumulative frequency distributions below corresponds to this frequency distribution

A. | B. | C. |

D. | E. |

**Q181.** Which threshold frequency distribution corresponds to the following description:

This population is divided between those who are very easily persuaded to participate - they will jump on bandwagon readily - and people who are very reticent to join a movement, with relatively few people in between.

A. | B. | C. |

D. | E. |

**Q182.** Which threshold frequency distribution corresponds to the following description:

The community has a few people who will join no matter what, a few more who will join if some others have joined, still more who will join if a goodly number are on board and so on all the way up to a hesitant few but even they will join if it appears everyone else has.

A. | B. | C. |

D. | E. |

**Q183.** In the election between candidate A and candidate B, for voter X it comes down to what the candidate will do for the elderly. The election is a toss-up and it may well come down to X's vote. Research indicates that candidate A is quite likely (75% chance) to do 4 things for the elderly but may only end up doing one thing (25% chance). Candidate B, on the other hand, is very unlikely to do 4 things (10%) but is 90% likely to do 2 things. For whom should X vote if this is the deciding issue.

**Q184.** A campaign director is flying blind. Two tossup states both have 20 electoral votes. All current information is that the chances of winning in each is 50:50.

Draw the event tree that describes the possible election outcomes.

Our campaign director has the opportunity to do one last ad buy of $1 million. Research and experience have shown that an ad buy in a right state where a significant portion of the electorate is still open minded could shift the odds of winning to 60/40. How do we know? We've done lots of audience research that shows how particular electorates respond to this ad's approach. But doing the ad buy in the wrong state (one where folks have really made up their minds) will have no effect on the outcome. What we don't know is which, if either, of these states is the best fit for this type of campaigning.

Draw this decision tree.

Now suppose there is a poll she could do to find out whether state A or state B is the more promising state for the new ad. There is a 50% chance the poll says state A and a 50% chance it says state B. If it says state A then you do the ad buy there and you are certain to increase your chances while things in B stay the same. And vice versa.

What is the value of the information the poll can provide, in electoral votes?

**Q185.** Sketch a causal loop diagram for these two systems (be sure to label each link and the overall loop). Comment on the long term equilibrium of this system.

- Being pro candidate X…
- …makes you give money…
- …makes the campaign send you emails…
- …makes you want to go to a rally…
- …makes pro candidate X…

- Being pro candidate X…
- …makes you give money…
- …makes the campaign send you emails…
- …makes you get fed up with the campaign…
- …makes you a little sour on candidate X…

- Not hearing much from the campaign…
- …makes you miss your candidate
- …makes you feel more pro candidate X

**Q186.** Our neighborhood Obama for America committee is an active one. It's so active that it wears people out. Over the course of the campaign it tends to recruit 4 new people every week but it also loses about 10% of its membership due to fatigue each week. The committee began in June with 6 members. Write the difference equations that describe the size of the committee (S) each week. What's the long term prognosis?

**Q187.** The diagram below represents a candidate's shifting weekly position on abortion. Treating this as a Markov model (where each transition is independent of previous sequence of states), show us what the transition matrix would look like. What do we call the state that would represent a candidate's final position on an issue? Using this diagram, what prediction can you make about what this candidate's position would be if he were to be elected?

**Q188.** "Women's issues" have been talked about a lot in the 2012 presidential campaigns. One issue has been the hiring of women in leadership positions in society. Draw a causal loop diagram to represent the following relationships.

The more "gender bias" the fewer qualified women there will be.

More qualified women means more women in positions of power.

The more women in power, the less "gender bias" in society.

Assuming we start with social bias and not many women in positions of power, how is this system likely to behave?

Now let's modify things a bit. Let's suppose we solve the "supply" problem and break the link between bias and the number of qualified women and that the latter grows significantly. We change our model slightly:

Societal bias produces social blindness to existence of qualified women.

This social blindness means fewer women will be in the pool that is considered for positions of power.

The fewer women in the pool, the fewer end up in positions of power.

And, as before, the more (fewer) women in power, the less (more) "gender bias" in society.

Draw this causal model.

Now let's add another causal relation: the fewer women in positions of power, the more NGOs emerge to promote women's participation in government, etc. The NGOs hit on a strategy called that the men in power call "binders of women" — whereby they do the legwork needed to show the men the qualified women that their bias made them blind to.

Add the NGOs and the binders to our causal model. Identify a balancing loop that might portend the achievement of improved gender diversity in positions of power.

**Q189.** Our campaign wants to hold a giant rally the Sunday before the election. Many voters are fired up, many are tired. Some think we can win, others not so sure. Suppose the ready-to-jump-on-the-bandwagon threshold distribution is shown below. The numbers here mean how many people are willing to come to the rally given different levels of expected participation.

Analyze this information and describe the direction our organizing strategy should go. What should we expect? How much intervention could produce how much of a desired result. Assume that our current research suggests about 40 people are currently planning on going to next week's event.

Threshold | Count |
---|---|

0 | 12 |

10 | 3 |

20 | 4 |

30 | 5 |

40 | 6 |

50 | 9 |

60 | 13 |

70 | 17 |

80 | 19 |

90 | 6 |

100 | 0 |

**Q190.** An eager campaign volunteer wants to think rationally about where to put her time. She does her research about phone-banking and canvassing and discovers the following.

A full shift (calling hundreds!) at phone banking has a 10% chance of producing 20 votes and a 60% chance of producing 2 votes, 10% chance of producing no votes and a 20% chance of losing 2 votes. Canvassing, by comparison, has a 20% chance of producing 8 votes, 30% chance of producing 4 votes, and a 50% chance of producing no votes. Other things being equal, which would be a better use of her time?

**Q191.** A voter has an objective function which is to minimize the difference between her positions on two issues and those of the candidates. Here positions can be described as a 3 on issue A and an 8 on issue B. Candidate 1 has positions -2 and 9 while candidate 2 has positions 4 and 4. For whom will the voter cast her ballot?

**Q192.** A student wants to maximize her GPA. Three of her courses are required 3 credit courses and she estimates she will get a B in each. She has a choice between an easier 3 credit course that she can definitely get an A in and a slightly harder 4 credit course in which she expects a B+. What will she do?

**Q197.** Explain and give an example of a *dominant strategy* in a prisoner's dilemma game.

**Q202.** (a) Set up the issue of whether to use the metric system or the English system of weights and measures as a coordination game. (b) Identify any equilibria and whether they are efficient or not. (c) If we are in the English/English cell, describe both players' motivations to unilaterally switch to metric. (d) what if we were in the metric/English cell?

**Q203.** Group these examples of coordination games and explain.

- do we store the ketchup in the fridge or in the cabinet?
- smokers should marry smokers and non-smokers should marry non-smokers
- cat people and dog people and dating
- people's sense of what constitutes rudeness
- infidelity is never OK, infidelity is OK in certain circumstances
- Erring on the side of caution; nothing ventured, nothing gained
- Every woman for herself; Let's work as a team.

**Q204.** Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. When two agents meet they may have all the same behaviors, none of the same behaviors, or 1 or 2 behaviors in common. Suppose the probability of interaction is proportional to their similarity. IF they do interact, they flip a coin and who ever wins gets imitated by the other agent.

In the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now)

A 1110 |
B 1010 |
C 0010 |
D 1001 |

E 0000 |
F 1111 |
G 1001 |
H 1011 |

I 1000 |
J 1000 |
K 1110 |
L 0000 |

M 0010 |
N 1100 |
O 0100 |
P 0111 |

**Q205.** Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. When two agents meet they may have all the same behaviors, none of the same behaviors, or 1 or 2 behaviors in common. Suppose the probability of interaction is proportional to their similarity. IF they do interact, they flip a coin and who ever wins gets imitated by the other agent.

Use the two random number tables below (the left table for doing a Monte Carlo simulation of whether interaction occurs and the left table to determine which agent is the leader and which is the follower) to work out the next state n the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now)

69 | 72 | 43 | 97 | 87 | 0 | 0 | 0 | 1 | 1 | |

37 | 86 | 35 | 23 | 41 | 1 | 1 | 0 | 0 | 1 | |

88 | 36 | 94 | 60 | 60 | 1 | 1 | 1 | 0 | 0 | |

84 | 26 | 3 | 87 | 12 | 0 | 0 | 1 | 1 | 0 | |

8 | 10 | 56 | 52 | 29 | 1 | 1 | 1 | 0 | 0 | |

26 | 5 | 30 | 15 | 58 | 0 | 1 | 1 | 1 | 1 | |

95 | 3 | 95 | 18 | 69 | 0 | 0 | 1 | 0 | 0 | |

71 | 42 | 55 | 64 | 21 | 0 | 0 | 1 | 1 | 0 | |

68 | 75 | 90 | 19 | 64 | 0 | 0 | 1 | 1 | 0 | |

75 | 13 | 77 | 1 | 89 | 0 | 0 | 0 | 0 | 0 |

A 1110 |
B 1010 |
C 0010 |
D 1001 |

E 0000 |
F 1111 |
G 1001 |
H 1011 |

I 1000 |
J 1000 |
K 1110 |
L 0000 |

M 0010 |
N 1100 |
O 0100 |
P 0111 |

**Q206.** Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. Further suppose that there is some pressure toward consistency such that having a "don't do" behavior next to a "do do" behavior is uncomfortable and so agents have some internal urge to change their behavior to be more consistent.

Let's say that a behavior that is the only one of its type (a 0 among three 1s, for example) has a 50 percent chance of switching to make the set fully consistent. Each behavior that's one of an even split (e.g., a 0 in a 0011 agent) has a 10% chance of switching. We can put it this way: there is a 10% chance the first behavior changes, 10% the second, etc. and 60% chance no change happens.

Use the two random number table below to work out the next state n the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now). For 50% chance use "random number above 50 = change, below 50 = stay." For the 10% chances, 0<10 is change first, 10<20 change 2, etc.

69 | 72 | 43 | 97 | 87 |

37 | 86 | 35 | 23 | 41 |

88 | 36 | 94 | 60 | 60 |

84 | 26 | 3 | 87 | 12 |

8 | 10 | 56 | 52 | 29 |

26 | 5 | 30 | 15 | 58 |

95 | 3 | 95 | 18 | 69 |

71 | 42 | 55 | 64 | 21 |

68 | 75 | 90 | 19 | 64 |

75 | 13 | 77 | 1 | 89 |

A 1110 |
B 1010 |
C 0010 |
D 1001 |

E 0000 |
F 1111 |
G 1001 |
H 1011 |

**Q207.** Convert the following logic into a set of step-by-step instructions in a manner that uses stepwise refinement.

To execute coordination we proceed as follows. Each agent will consider in turn its north, east, south, and west neighbors. First the agent determines whether interaction will take place at all based on similarity. Then, if they do interact, they flip a coin to decide who is the leader and who is the follower. Then the follower copies the traits of the leader. And then onto the next neighbor if there is one.

We can incorporate the following design decisions into our model: (1) neighbors who have already interacted in a given round do not do so again; (2) an agent can change multiple times during a given round; (3) all interactions are with the agent's current state.

**Q219.** Translate the following into inequalities.

- I can only I spend as much cash as in my wallet on dinner, dessert, drinks, and a tip and I really want to have dinner and drinks though I might pass on dessert.
- You are managing a youth shelter. Kids present with an array of personal challenges, each of which require different levels of attention from your staff. Clients with issue A require 4 hours of attention per week. Issue B, about 2 hours, C requires 16, and D 7. Your budget allows you to staff 75 hours per week.
- Breakfast is some eggs, some pancakes, some bacon. You have to have at least twice as many pancakes as eggs. You can't have fewer than 2 strips of bacon.

**Q220.** What is the objective function in each of the following situations?

- What is the largest volume box I can make by folding a piece of cardboard that is A inches by B inches?
- Pancakes cost $1 each, eggs are 1.50, and blintzes are 2. Pancakes have 200 calories, eggs 125 and blintzes 450. What combination gives me the most calories for 5 dollars?
- What's the cheapest 1000 calorie daily diet?
- I have information on the level of AOD demand reduction we can expect from public awareness campaigns, DARE visits to public schools, increased treatment slots, and increases in after care. I know the cost of each type program and I have a limited budget. What mix of programs should I institute to have the biggest effect on demand?

**Q221.** For each of the problems described below, say whether it is best thought of as an analog to diet, transport, activity, or assignment as outlined above.

- S&Z problem #1 Incinerators DIET TRANSPORT ACTIVITY ASSIGNMENT
- S&Z problem #2 Police Shifts DIET TRANSPORT ACTIVITY ASSIGNMENT
- S&Z problem #3 Hospitals and disasters DIET TRANSPORT ACTIVITY ASSIGNMENT
- S&Z problem #4 Electricity generation and pollution DIET TRANSPORT ACTIVITY ASSIGNMENT
- S&Z text example – transit maintenance DIET TRANSPORT ACTIVITY ASSIGNMENT

**Q222.** Write out the sample problems on pp 190-2 with explanatory solutions.

**Q223.** A non-profit supplier of after-school materials has orders for 600 copies from San Francisco and 400 copies from Sacramento. The organization has 700 copies in a warehouse in Novato and 800 copies in a warehouse in Lodi. It costs $5 to ship a text from Novato to San Francisco, but it costs $10 to ship it to Sacramento. It costs $15 to ship from Lodi to San Francisco, but it costs $4 to ship it from Lodi to Sacramento. How many copies should the organization ship from each warehouse to San Francisco and Sacramento to fill the order at the least cost? [http://www.sonoma.edu/users/w/wilsonst/Courses/Math_131/lp/default.html]

**Q224.** You are working for an agricultural cooperative which is helping local farmers figure out how to optimize the mixture of crops they plant. A typical farmer has 10 acres to plant in wheat and rye. She has to plant at least 7 acres. However, she has only the equivalent of $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the expected profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits? (From Steve Wilson)

**Q225.** Your are the supervisor at a new after-school program. The program will serve 100 boys and 100 girls. Activities will include chess, games, and crafts. Materials, supervision, and the like have been priced out at $2/person for chess, $10/person for games, and $5 for crafts. Space needs are such that we can get 8 chess players at a table, 4 games players, or 2 crafters. The center has 50 tables. Solid research has shown that activity preferences among this population of children is somewhat gender specific. Boys and girls like chess the same but games are 70% girls and 30% boys while crafts tend to be 30% girls and 70% boys. What is the most economical division of activities subject to these constraints?

**Q226.** "You have $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts?" (From PurpleMath.com)

**Q227.** A gold processor has two sources of gold ore, source A and source B. In order to kep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? (From Steve Wilson)

**Q228.** A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost. (From VITutor)

**Q229.** Bob builds tool sheds. He uses 10 sheets of dry wall and 15 studs for a small shed and 15 sheets of dry wall and 45 studs for a large shed. He has available 60 sheets of dry wall and 135 studs. If Bob makes $390 profit on a small shed and $520 on a large shed, how many of each type of building should Bob build to maximize his profit? (From solution here)

**Q230.** A store wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants which will sell for $30. Offer B is a package of three shirts and a pair of pants, which will sell for $50. The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B. How many packages of each do they have to sell to maximize the money generated from the promotion? (From VITutor)

**Q231.** A transport company has two types of trucks, Type A and Type B. Type A has a refrigerated capacity of 20 m3 and a non-refrigerated capacity of 40 m3 while Type B has the same overall volume with equal sections for refrigerated and non-refrigerated stock. A grocer needs to hire trucks for the transport of 3,000 m3 of refrigerated stock and 4 000 m3 of non-refrigerated stock. The cost per kilometer of a Type A is $30, and $40 for Type B. How many trucks of each type should the grocer rent to achieve the minimum total cost?

Alternatively

A school district has two types of lower division schools, type A and type B. Type A school buildings have capacity for 200 little kids and 400 big kids. Type B buildings have capacity for 300 little kids and 300 big kids. Next year the district expects enrollments of 3000 little kids and 4000 big kids. Type A buildings cost 30,000 per year to maintain while type B buildings cost 40,000. What mix of school buildings will allow the district to handle the expected enrollment at the lowest maintenance cost? (From VITutor)

**Q239.** I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test (total cost = prep course + twice the exam fee). Should I take the prep course??

**Q240.**This is an event tree problem, that is, there are no choices to be made. Work out the probabilities of each of the final outcomes.

There is a 72% chance that candidate A will win the presidency over candidate B. There is a 55% chance that candidate A's party will win control of the senate and a 30% chance that his party will win control of the house.

**Q241.** If my new study method works, I should earn a 98 on the test. If it does not work, I will get a 79. Research suggests that there is a 75% chance it works. What is the expected value of my grade?

A. |
87.5 | B. |
93.25 | C. |
95.5 | D. |
79 | E. |
98 |

**Q242.** Draw a flowchart that represents the following protocol for enjoying a Saturday afternoon.

If it is sunny, go to the beach. If it is not sunny go to the movies.

If you go to the beach, if you are by yourself, take an umbrella and a good book. If you are with friends, take a bottle of wine and some nice cheese.

If you go to the movies alone, buy a monster popcorn and sit right up front. If you go with friends, be more restrained with the snacks and sit midway back.

Have a nice dinner afterwards.

**Q243.**Consider the following instructions for funding your NGO and then draw a flow chart representing this logic

Write the grant. Find a funder. Submit the grant. Wait to see if it is funded. If it is funded, start the project. Otherwise go back to finding a funder.

**Q244.**This question extends problem 243. You've learned the following things during your professional training. Represent this information as a three level stepwise refinement.

- Preparing to write a grant consists of identifying a need and putting together a logic model that shows what new inputs are needed to generate desired outcomes
- Finding a funder requires identifying a list of funders, looking up the kinds of projects they are funding, and finding matches for your project
- Writing a grant involves (1) preparing to write the grant; (2) finding template appropriate to particular funders; (3) producing drafts and reviewing with staff
- Draft and review protocols vary, but one you like is to produce a draft, post it on Google docs for the team to comment on, send a prodding email to team members every few days until it looks like there are no more comments on that draft, make revisions and repeat this process until the deadline is near.

**Q245.** Offer a critique of this flow chart diagram

**Q246.** What's wrong with this flow chart? How would you fix it?

**Q247.** What's wrong with this flow chart? How would you fix it?

**Q248.** What criticism would you offer if the diagram below were my first stab at a flow chart for an organizational process? How would you fix it?

**Q249.** Translate each of the flow charts below into everyday English.

**Q250.** What's wrong with this flow chart? How would you fix it?

**Q251.** Suppose the (time) cost of waiting behind someone with a big shopping cart in the super market checkout line is 10 minutes while the time behind someone with a very few items is 2 minutes. Consider three cities, A, B, and C. Suppose the probability of running into someone again soon in the grocery store is 0.1, 0.2, and 0.4 in cities A, B, and C, respectively. What do we predict? Which "path to cooperation" does this illustrate?

**Q252.** Consider this network in which green agents are cooperators and violet are defectors and the cost of cooperating is 2 while the benefit of being cooperated with is 5. Where is the equilibrium is people's behavior changes based on their network experiences?

**Q253.** Consider this network in which green agents are cooperators and violet are defectors and the cost of cooperating is 2 while the benefit of being cooperated with is 5. Where is the equilibrium is people's behavior changes based on their network experiences?

**Q254.** Just based on reasoning, explain the relation among relatedness, cost of cooperation, and benefit of cooperation in kin selection as a mechanism for achieving cooperation in the face of prisoner's dilemma scenarios.

**Q255.** Work through the section on direct reciprocity in Nowak and Sigmund, "How Populations Cohere."

**Q256.** Consider the collective action model described in Lecture 17.4: Collective Action and Common Pool Resource Problems where $x_j$ is the cost to me to "pitch in" and do my part in some collective effort. Each member of the collective reaps benefits from the contributions of those who decide to pitch in. In particular, they receive some fraction $\beta$ of all the contributions. Their net benefit is thus, this amount minus the effort they contribute. In other words,

Suppose you are in a class of 21 students and everyone is expected to prepare for class in a manner that costs 1 unit of life. In the class itself, things go much better when people are prepared and we estimate that the benefit a student derives from the class is equal to 0.2 units of life for each person who comes prepared.

(a) What is your net payoff if you do the reading half the class rest of the class comes prepared too?

(b) What is the benefit to a shirker under the same conditions?

(c) How many people do you need to think are going to do the reading to make it worth it to do the reading?

**Q257.** (a) Explain the equations for common pool resource problems as discussed in Lecture 17.4: "Collective Action and Common Pool Resource Problems":

$x_j$ : amount consumed by person j

$X$ : total consumed

Amount available next period: $C_{T+1} = (C_T - X)^2$

(b) Propose values of these variables that would result in a steady state equilibrium value of the resource.

**Q258.** Insofar as particulars matter, what's the difference between cows, lobsters, and whether you live up stream or downstream?

**Q259.** What are the 5+2 means of achieving cooperation in the face of structural arrangements that "mandate" non-cooperation in human relationships?

**Q260.** Explain how "group selection" can give rise to cooperative behavior in human society.

**Q321.**: Our consulting firm, NGOsRus, has developed a new organizational assay protocol to help characterize the financial health of community organizations. We have tested the instrument on many organizations whose financial well-being has been determined by other, much more expensive means. Here's what we know:

Healthy organizations pass the test 80% of the time but fail it 20% of the time. Unhealthy organizations fail the test 88% of the time but pass 12% of the time.

How likely is it that an organization that passes the test is, in fact, in good state financially?

**Q322.** Say what's wrong with these flow charts and redraw them correctly.

**Q323.** What flow chart concept does this diagram illustrate? Explain what it means and how we use it. Draw the series of flow charts implied by this diagram.

**Q324.** You are the board chairperson of a small non-profit and you are hiring new executive director. It has come down to two candidates, one rather plain vanilla and, frankly, a bit boring, but rock solid, and the other quite exciting and edgy. After all the interviews and due diligence, you and your board estimate that that with the boring candidate there is a 94% likelihood that she'll be OK, a 5% chance that she'll be amazing, and a 1% chance that she'll be a disaster. You estimate the "value" of OK to be 25, the value of amazing to be 100 and the value of disaster to be -100.

(A) What is the expected value of hiring the boring candidate?

The board estimates that there is a 60% chance that the edgy candidate is amazing and a 40% chance she will be a disaster.

(B) What is the expected value of hiring the edgy candidate? Other things being equal, what is the best decision here?

A consultant friend of your tells you about a personality test that you can administer to job candidates that helps distinguish between those likely to be amazing and those likely to be a disaster.

(C) With the above assumptions, how much would it be worth to have this test to use on your edgy candidate (the test would tell you for sure whether this particular edgy person is the amazing or the disaster type)?

But suppose it's not a perfect test, but it's pretty good. It turns out that with candidates who really are amazing it gets it right about 75% of the time. With those who are actually disasters waiting to happen, it gets that right 90% of the time.

(D) If the test were administered to our edgy candidate and she passed, how likely is it that she'd be amazing? And if she failed, how likely she was actually a disaster?

(E) How much would we be willing to pay for the imperfect test?

**Q325.** Have a look at the paper shown below about immunization in Uganda. Look especially at the causal loop diagrams on pages 102(146) and 103(147). Explain what is going on in each of the labeled/shaded loops. In some cases, there might be a sign missing. Based on your reading of the diagrams, supply these and explain.

## R1:

## B1:

## B2:

**Q326.** (A) Consider this plot of P_{n+1} vs. P_{n}. Without worrying about what sort of system it might be, show that you understand how the chart works by describing the behavior of this system if it starts at time i at P_{i}=30. How about 70?

(B) If this is a model of attendance at, say, a protest rally with the axes representing percentage of the population, and P_{n} is how many showed up last week (a number everyone knows) and P_{n+1} is how many that means we can expect this week (based on the distribution of individual thresholds - how many people need to be going for me to decide to go), how would you interpret the gaps A and B on the chart?

(C) Think about the "standing ovation model." What features does it add to the basic model described here.

**Q327.** Our agency provides three types of client service: A, B, and C. And we have 3 kinds of staff: X, Y, and Z.

Each type A service requires 3 hours of an X staff member's time and 1 hour of a Y. Type B requires 2 X, 1 Y, and 3 Z hours. And type C requires 1 X, 3 Y, and 2 Z.

Currently we have 2 X, 1 Y and 1 Z on staff. We pay X's $25 per hour, Ys get $30 and Zs get $40. Assume everyone works a 35 hour week. At 35 hours per week our labor costs are 4200.

Revenue from type A service is $100, B is $200, and C is $300.

Regulations require that we serve at least 5 of each client type each week and that we serve at total of at least 21 clients each week.

What client mix will allow us to maximize revenue?

**Q328.** Have a look at this recent release from Bureau of Labor Statistics (BLS). The data separates those without a job into unemployed but "in the labor force" and "marginally attached to the labor force" and a subset of these called "discouraged" - the former would like to work but have not looked in the last four weeks and so are not counted as unemployed. The latter are not actively looking for work having given up on the idea that its possible to find. These groups are **not** included in the denominator when the unemployment rate is calculated. The simple version of the unemployment rate is, then,

Some recent op-eds have counseled caution about optimism that the overall unemployment rate has been going down because it might reflect growth in the number of people no longer looking for work. We'll think about that with a Markov model. We'll simplify the states a worker can be in:

- employed (E)
- short term unemployed - 14 weeks or less (US)
- long term unemployed - over 14 weeks (LS)
- Marginally attached to the labor force - no longer looking for a job (MALF)

Let's construct a simplified Markov model of unemployment based on transition rates shown here:

If the unemployment rate is calculated as the ratio of those who are short term unemployed (US) plus those who are long term unemployed (UL) to the total labor force (E + US + UL), how would things evolve over the next twelve months if the starting numbers are these:

What will the unemployment rate be? Even if it is agreed that getting unemployment to near 6% is a policy goal, are there reasons the results might not be a cause for celebration?

Create a chart showing changes over the next 12 months. Suggestion: plot total employment (E) on secondary axis since it's such a large number. In the alternative, put it on a separate chart.

**Q329.** Create for yourself a one page cheat-sheet/course summary illustration that captures what you have learned/want to take away from the course. Be prepared to show it at oral exam and explain it to instructor as if he were a fellow student who has not taken this course. This can take any form at all within the constraints of being no more than one sheet of paper. Just for fun, here are some examples from other courses: Social Theory, GIS, Social Control. Focus, of course, on content, not artistic flair.

**Q330.** **Equilibrium** came up many times in this course. Briefly catalog several and describe the concept and its importance. Be sure you can address (1) whether it is a normative concept (2) stable vs. unstable (3) different examples.

**Q331.** Studying for an exam could raise a student's grade by a whole letter grade. But it turns out to not be a sure thing. Suppose research has shown that six hours of studying has a 60% chance of increasing your grade by one letter grade, a 25% chance of having no effect, and a 15% chance of actually lowering it by one letter grade (perhaps due to increased anxiety and not enough sleep).

Calculate the expected value of the investment of 6 hours of study time in terms of "letter grades per hour."

**Q410.** Show what you know about Schelling's "micromotives macrobehavior" models by explaining this diagram.